I'd have to say my favorite games are Resident Evil 4, the God of War series, and the Metroid Prime series. And like a million others... like Metal Gear Solid. And I have to admit that I never get tired of running people over in Grand Theft Auto 4. I also enjoy the Final Fantasy series.
Basically, I like games that are challenging and fun, but I also enjoy anything with an immersive story. Puzzle-solving is really fun too. Good play-control is a must.
I'm not playing anything at the moment, but I'll probably play Half-Life 2 next, including Episode 1 and 2. I go through phases where I don't play any games for months, then I will play a bunch of games straight for a few weeks. That's how I take vacations.
I also enjoy playing regular nintendo games because of the simple gameplay. To sum it all up, I LOVE VIDEO GAMES. Sorry that this post is all over the place!